US11033006B2 - Hydrodynamic treadmill: a tracking device to study biotic/abiotic systems in gravitational and hydrodynamic fields - Google Patents
Hydrodynamic treadmill: a tracking device to study biotic/abiotic systems in gravitational and hydrodynamic fields Download PDFInfo
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- A—HUMAN NECESSITIES
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- A01K—ANIMAL HUSBANDRY; AVICULTURE; APICULTURE; PISCICULTURE; FISHING; REARING OR BREEDING ANIMALS, NOT OTHERWISE PROVIDED FOR; NEW BREEDS OF ANIMALS
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Definitions
- This invention relates to observation and tracking of moving objects in a fluid.
- a hydrodynamic treadmill that effectively provides unlimited scope for vertical motion.
- a water-filled wheel with a horizontal axle provides such a treadmill, where rotation of the wheel provides vertical motion of the water that compensates the motion of the particle or organism being observed, thereby keeping it within the field of view of an optical system disposed at a fixed location. In this manner, the above described difficulties with conventional observation approaches are avoided.
- This work provides a methodology/tool to track and observe micro/mesoscale (1 ⁇ m to 1 mm) biotic and abiotic systems under the influence of a gravitational field and hydrodynamic forces.
- the main purpose of this work is that it enables observations to be made over long time (tens of hours to days or months) and length scales (hundreds of meters) which have been hitherto not possible given the practical challenges of bridging the vast difference in scales between the observed entity (small scale) and the observation volume.
- Representative example systems include oceanic microorganisms, marine snow, microscopic particles such as drops falling undergoing sedimentation in air or water.
- this device also makes possible study of uniform flow past micro/mesoscale objects of non-neutral buoyancy (objects that rise/sink in an ambient fluid). Studying uniform flow past different kinds of objects such as spheres, drops, cylinders etc., is a foundational experimental tool in the fields of fluid mechanics and transport phenomena. Traditionally this is achieved using a wind or water tunnel wherein a uniform flow is maintained in a certain test section.
- fundamental limitations of fluid mechanics impose a certain minimum limit on the size of this test section which is around a meter. This also imposes a limitation on the minimum size of objects that can be studied within this test section due to fundamental limitations of high numerical aperture optical systems. This means that it is typically challenging to study uniform flow past objects which are less than a millimeter in size.
- This device offers a solution to these problems using an implementation of a circular boundary-less geometry.
- This approach one can lower this fundamental size limit to study uniform flow past objects which are 10-100 micrometers or lower in size. This makes possible the study of a whole class of fundamental fluid mechanics and transport phenomena which have been hitherto impossible to observe.
- the system can be compact (20 cm in size) and may be integrated seamlessly with conventional microscopes as a replacement tracking stage, yet allows motions of hundreds of meters to be observed, a scale of observation that has been hitherto impossible.
- long-time tracking and microscopy of marine microorganisms is important for marine ecology, biological oceanography, physical oceanography and is specifically applicable to phytoplankton, zooplankton, larvae of marine organisms, and marine snow dynamics.
- Observing sedimenting microparticles and microdroplets is important in atmospheric sciences and is specifically applicable to cloud formation, rain drop coalescence mechanisms, and aerosol particle dynamics.
- Observing growth of microcrystals in a fluid is important for materials science and is specifically applicable to understanding the role of fluid flow on crystal structure.
- Observing three-dimensional fluid flow is important for fluid mechanics and is specifically applicable to mapping the three-dimensional flow around an object moving under the combined influence of gravity and/or its own motility.
- FIG. 1 shows an embodiment of the invention.
- FIG. 2 shows another embodiment of the invention.
- FIGS. 3A-D show operation of focus control in connection with embodiments of the invention.
- FIGS. 4A-B show control of radial position of the object and of object orientation.
- FIG. 5 is a comparison of results of the present work with a conventional measurement technique for velocities of beads falling through a fluid.
- FIGS. 6A-B show tracking results as obtained from an embodiment of the invention.
- FIGS. 7A-B show further tracking results as obtained from an embodiment of the invention.
- FIGS. 8A-B show further tracking results as obtained from an embodiment of the invention.
- FIG. 9 shows further tracking results as obtained from an embodiment of the invention.
- FIGS. 10A-C show further tracking results as obtained from an embodiment of the invention.
- FIGS. 11A-B schematically show how chemical concentration in the sample chamber can be varied according to virtual depth.
- FIG. 12 shows an embodiment of the invention configured as a controllable stage for use with a conventional microscope.
- this work provides a boundary-less, fluid-filled geometry and closed-loop image processing and tracking to observe biotic and abiotic systems whose motions have a significant vertical component owing to the effects of gravity, hydrodynamics and active motility.
- a circular geometry which is implemented as a wheel with a fluid-filled annulus, effectively makes one of the dimensions periodic and boundary-less, meaning that the particle or organism under observation can freely move in that direction without being hindered by a wall (see FIG. 1 below).
- a closed-loop tracking method is implemented such that when the object moves with respect to the fluid, in a net vertical direction, the wheel moves in the opposite sense so that the object is kept within the field-of-view at all times.
- this angular motion is well-approximated as a linear motion and the dynamics are unaffected by the tracking motions of the wheel. Tracking in the two other orthogonal directions can be implemented using linear motion on top of this long-time tracking along the vertical direction using angular motion.
- FIG. 1 shows an exemplary embodiment of the invention, which is an apparatus for observing unbounded motion of an object 106 in a fluid 104 .
- an optically transparent sample chamber 102 is configured as an annulus filled with fluid 104 .
- An azimuthal control system 114 is configured to rotate sample chamber 102 to compensate for azimuthal motion 108 of object 106 in fluid 104 such that object 106 continuously remains visible within a predetermined field of view 110 .
- arrows 112 schematically show the rotation of sample chamber 102 provided by azimuthal control system 114 .
- sample chamber 102 is often referred to as a wheel in this description.
- the azimuthal motion control can be carried out by a fine stepper motor/rotational stage that applies rotational movements to the wheel.
- This idea can be extended to compensate for any external bias field capable of inducing anisotropic motion of the object directly (e.g., abiotic particle falling through a fluid) or indirectly (e.g., a biological organism swimming up or down with respect to gravity).
- the direction along the bias field is made boundary-less by implementing an annular fluidic geometry and choosing the field of view appropriately. Movements of the object in the direction of the bias field are compensated by rotational movements of the wheel.
- azimuthal motion of the object is defined as motion of the object around the circle of the sample chamber. In laboratory coordinates, this can be thought of as being tangential motion (z directed motion on the figures, for the field of view as shown).
- the time duration of object tracking is unlimited in principle, e.g., from milliseconds to a month.
- Object 106 is unrestricted in its vertical motion, enabling long tracks (up to hundreds of meters) to be observed.
- the tracking procedure ensures that the object can undergo large relative displacements in the direction of the potential field while being stationary (in the potential field dimension) in the lab reference frame.
- the device ensures that the object can be imaged at high spatial and temporal resolution since the optical setup need not move to track the object.
- the wheel preferably has an inlet and outlet port to fill and drain fluid from the wheel.
- the material used to fabricate the wheel is chosen to be optically clear in the plane of the wheel.
- the field of view where the object of interest is tracked is preferably 90 degrees from the vertical symmetry axis of the wheel (e.g., 110 and 116 on FIG. 1 ).
- the inner and outer rims of the annulus are preferably made from materials with high thermal inertia to stabilize thermal flows in the fluid inside the wheel.
- Such objects include, but are not limited to: biotic objects, abiotic objects, neutrally buoyant objects, non-neutrally buoyant objects, and objects having a size of 1 mm or less.
- the object size can be from 100 nm-5 mm. Smaller or larger objects require a suitable change in the optical assembly as well as the dimensions of the wheel.
- the wheel diameter can be from 10 cm-50 cm. Larger wheel diameters allow a closer approximation of the motion to linear motion. Smaller wheel diameters are suitable for more portable applications.
- the angular velocity range of the wheel can be from 100 ⁇ rad/s-0.1 rad/s. This range depends on the slowest and fastest motions that need to be tracked by the wheel.
- the fluid viscosity can be about 0.001 Pa s (the viscosity of water). Water is the most typical fluid for biological measurements, however the operating principles of the device would remain unchanged for other viscous fluids.
- the fluid density can be 1000 kg/m ⁇ circumflex over ( ) ⁇ 3 (water), Other lighter or denser fluids can also be used based on the application. Fluid density can be modulated to change the relative velocity between a sedimenting object and the fluid. This is an important parameter to change the particle Reynolds number in fluid mechanics studies.
- FIG. 2 shows an example of this approach, along with several optional features of preferred embodiments. These optional features can be practiced individually or in any combination.
- 202 is ambient light control
- 204 is an inlet for an onboard pump
- 206 is a liquid lens or fast actuator for rapidly changing the focal plane of the optical system (as discussed below in connection with FIGS. 3A-D )
- 208 is a microscope objective
- 210 is a linear actuator for radial motion control (x direction on FIG. 2 )
- 212 is a linear actuator for focus control (y direction on FIG.
- 214 is an actuator for rotating sample chamber 102
- 216 is a camera (optionally including a z-directed actuator as shown)
- 218 is an image processing system connected to camera 216 and light 202
- 220 is motion controller connected to actuators 210 , 212 , 214 and to any actuator that may be present in camera 216 .
- the entire assembly is surrounded by a thermal enclosure (which may or may not be under active temperature control) within which the sample chamber and the optical observation system are enclosed. This serves the dual purpose of reducing thermally driven flows in the annular fluid and also allowing controlled illumination.
- the radial motion control and the focus motion control can be any combination of open-loop control and closed-loop control.
- radial motion control and focus motion control of a relative position of the sample chamber and the optical observation system are provided.
- the tracking movement along the X and Y directions can be carried out by linear actuators which move the optical assembly.
- FIG. 11 shows an alternative configuration where these actuators move the sample chamber instead of the optical assembly.
- the object can be imaged using an optical unit having a suitable combination of lenses based on the optical resolution desired and the object being observed.
- the optical unit can be modular and can be easily swapped out to image objects of different sizes (microns to mm) and at different optical resolutions.
- the images can be collected using a camera and processed using an image processing unit (in particular a computer CPU or GPU).
- the images from the camera can be processed to extract the location of the object.
- Command signals can be sent from the image processing unit 218 to the motion control unit 220 which moves the Z, X and Y stages to compensate for the object's motion.
- Tracking along the Z and X directions can be performed using the object position as extracted from the 2D image.
- Tracking along the Y direction (optical axis) can be carried out using a method detailed below.
- the tracking in the Z-direction is carried out by both the wheel (via actuator 214 on FIG. 2 ) as well as a smaller linear actuator that couples to the optics assembly ( 216 on FIG. 2 ).
- the smaller linear actuator handles the high frequency (e.g., 10-100 Hz) movements of the object while the wheel handles the lower frequency (e.g., 0-10 Hz) movements of the object. This allows objects which have a high-frequency movement to be studied over long length and time-scales without modifying the behavior due to the tracking.
- the frequency range for the azimuthal motion control is from 0-10 Hz.
- the frequency range for the translational motion control is from 10-100 Hz.
- FIG. 3A shows a schematic of a preferred focus-tracking method, where the focal plane of the imaging system is scanned rapidly to capture a series of images at different focal planes.
- a fast actuator or liquid lens ( 206 on FIG. 2 ) is used to rapidly modulate the focal plane of the optical system.
- a focus-metric is calculated in real-time and the stage is offset to the location that maximizes this metric.
- a gradient climbing algorithm can be used to estimate the focal depth corresponding to the local maxima of this metric.
- the Y-stage is offset by the amount which is the error between the current position and the focal depth calculated in the previous step.
- FIG. 3B shows an exemplary fall-off of the focal metric as the focal plane moves away from the object position.
- FIG. 3C is a numerical simulation showing the focus-tracking method in action. The dashed curve represents the simulated trajectory of the object, and the symbols represents the position of the stage as it tracks the object.
- FIG. 3D is a plot of the focus-measure as a function of time which is used by the algorithm to estimate the object position.
- the focus motion control is based on scanning a focal plane of the optical observation system in a focus range and adjusting the relative position of the sample chamber and the optical observation system such that the object is in best focus at a predetermined point of the focus range as the object moves.
- FIG. 4A shows how a set-point for the azimuthal position of the object can be selected to cause the object to move radially within the sample chamber due to the ambient gravitational field, whereby both azimuthal and radial control of object position is provided. For example, if the object is moving down on FIG. 4A , then having a set point 402 above the 90 degree dashed line will cause the object to move inward radially. Similarly, having a set point 404 below the 90 degree dashed line will cause the object to move outward radially. If the object were moving upward on FIG. 4A , then set points 402 and 404 would have outward and inward radial motion, respectively.
- FIG. 4B schematically shows how the orientation of the object can be changed by generating shear in the fluid via angular acceleration of the sample chamber. As shown on the figure, such acceleration of the sample chamber can lead to a non-uniform fluid velocity profile within the sample chamber, which can act to rotate object 406 as shown. For a given object size and shape, the orientational trajectory can be known analytically hence allowing one to flip objects in a controlled manner.
- FIG. 5 shows results of a test of this approach.
- the working principle was tested by measuring the sedimentation speed of Density Marker Beads (Cospheric Inc.) of precisely calibrated density using the device to track the beads. Note that in this experiment the beads are stationary in the lab reference frame since the device applies a counter rotation that exactly balances the sedimentation rate. As a control experiment the same beads were tracked while they sediment in a tall cuvette past a fixed optical setup. In this case the beads are not stationary in the lab reference frame and the sedimentation speed is obtained by image processing to calculate the bead position as a function of time.
- the plot shows the results from both these experiments compared along with the theoretical predictions (mean: symbols, one standard deviation range: solid lines). This comparison shows that the device accurately measures the sedimentation speed and is able to distinguish even small variations in density of around 0.02 g/cc.
- FIGS. 6A-B show tracking of Pyrocystis fusiformis .
- Vertical migration data for Pyrocystis fusiformis were recorded using this approach.
- FIG. 6A shows a series of snapshots spaced apart by a minute of the organism as it migrates vertically.
- FIG. 6B is a plot of vertical displacement of Pyrocystis fusiformis as a function of time.
- FIGS. 7A-B show tracking of Volovox aureus , a common freshwater colonial algae, recorded using this approach.
- FIG. 7A shows a series of snapshots spaced apart 2 seconds of the organism as it migrates vertically and also rotates about its body axis. Note that microscopic details such as the daughter colonies within the main colony are clearly visible.
- FIG. 7B shows a 3D track of Volovox aureus measured using this approach.
- the radial motion control, the focus motion control and the azimuthal motion control can be combined to provide a 3-D volumetric scan of motion of the object.
- FIGS. 8A-B shows vertical migration data recorded using this approach.
- the plots shows the vertical displacement of Daphnia magna , a common freshwater organism, as a function of time.
- the total duration of the track is around 15 minutes in FIG. 8A during which the organism swims down more than 2 meters.
- FIG. 8B the organism swims upwards against gravity.
- the inset in FIG. 8A shows the organism as observed with the device.
- FIG. 9 shows vertical migration data recorded using this approach.
- the plot shows the vertical displacement of the larval forms of Patiria miniata (Starfish), a marine organism, as a function of time.
- the total duration of the track is around 5 minutes during which the organism swims downwards.
- the inset shows the organism as observed on the device.
- FIGS. 10A-C show 3D tracking results for freely swimming marine invertebrate larvae obtained using this approach.
- FIG. 10A shows results for Ophiuroidea (Brittle Star) larvae.
- FIG. 10B shows results for D. excenricus (Sand dollar) larvae.
- FIG. 10C shows results for A. parvimensis larvae (Sea Cucumber).
- FIG. 11A is a schematic of an embodiment as used for exposing an object to a varying environmental condition such as ambient chemical concentration/temperature.
- sample chamber 1002 includes a system for varying environmental parameters of the fluid as a function of a virtual depth as the virtual depth varies according to azimuthal motion of the object.
- this system is schematically shown by reservoirs I, II, III and IV having varying chemical concentrations as shown on FIG. 11B .
- reservoirs I, II, III and IV having varying chemical concentrations as shown on FIG. 11B .
- the wheel rotates the object will experience different chemical concentrations according to total vertical distance traveled.
- virtual depth is an artificial depth based on the total vertical distance compensation provided by the system for an object being observed in the hydrodynamic treadmill. This distance compensation is the wheel radius times the net total angle through which the wheel has rotated, accounting properly for multiples of 360 degrees.
- a new class of biological experiments can be performed by altering environmental parameters as this virtual depth varies. This allows for direct observation of the behavior of a biological organism (e.g., plankton) as it moves vertically through tens or even hundreds of meters, and for providing appropriate depth cues to the organism for such observation.
- the environmental parameters that can vary with virtual depth can include one or more of: optical intensity, optical spectrum, optical polarization, nutrient concentration, oxygen concentration, chemical species concentration, pressure, electric field direction and intensity, and magnetic field direction and intensity. This provides modalities to study influence of slow temporal and spatial (ecologically relevant) gradients of light, chemical concentration, salinity, temperature etc.
- Intensity, spectrum and polarization can be encoded as a function of virtual depth.
- an external light source e.g., 202 on FIG. 2
- Chemical Local variations in chemical concentration (e.g., of nutrient, oxygen, and/or odorant cues) can be introduced by using small volumes of chemicals stored on-board the wheel and released into the annular fluidic chamber at a particular virtual depth. This can be done using on-board micro-pumps to slowly modify the local chemical concentration, as schematically shown on FIG. 11A . Such a capability will be especially relevant for running behavioral assays to understand effects of various chemicals on organismic behavior.
- chemical concentration e.g., of nutrient, oxygen, and/or odorant cues
- Pressure can be modified by applying a static pressure to the fluid in the chamber whose intensity is modulated as function of virtual depth.
- Electromagnetic fields Different intensities and directions of electromagnetic fields can be applied as a function of virtual depth by suitable arrangements of devices like Helmholtz coils.
- FIG. 12 shows an alternative embodiment where the optical observation system is a horizontally mounted microscope (objective 1202 , body 1204 and eyepiece or camera 1206 ), and where all control of relative position of the optical observation system and the sample chamber is provided by motion of the sample chamber via stage controller 1208 .
- 102 is the rotatable sample chamber seen in a side view. This configuration is more suitable for applications where the device is used as a standalone microscope stage for retrofitting a conventional microscope.
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US7498551B2 (en) | 2006-10-06 | 2009-03-03 | Los Alamos National Security, Llc | Apparatus and method for tracking a molecule or particle in three dimensions |
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